I believe the ability to select individual entries, an entire page, or the entire log of battle reports to perform actions on (such as Mark as Read, Delete, etc) would be beneficial as it can grow quite large over time. Aside from the ease of cleaning it up, it would save the space on your side where the logs are stored as well.
In the last 5 days, I've made it up to 18 pages of battle reports (deleted any before that) and that is sending one attack at a time. Now sending multiple attacks, I can easily double that, and more in time.